Modelling female reproductive function in farmed animals

Model-based exploration of the impact of glucose metabolism on the estrous cycle dynamics in dairy cows

BACKGROUND

Nutrition plays a crucial role in regulating reproductive hormones and follicular development in cattle. This is visible particularly during the time of negative energy balance at the onset of milk production after calving. Here, elongated periods of anovulation have been observed, resulting from alterations in luteinizing hormone concentrations, likely caused by lower glucose and insulin concentrations in the blood. The mechanisms that result in a reduced fertility are not completely understood, although a close relationship to the glucose-insulin metabolism is widely supported.

RESULTS

Following this idea, we developed a mathematical model of the hormonal network combining reproductive hormones and hormones that are coupled to the glucose compartments within the body of the cow. The model is built on ordinary differential equations and relies on previously introduced models on the bovine estrous cycle and the glucose-insulin dynamics. Necessary modifications and coupling mechanisms are thoroughly discussed. Depending on the composition and the amount of feed, in particular the glucose content in the dry matter, the model quantifies reproductive hormones and follicular development over time. Simulation results for different nutritional regimes in lactating and non-lactating dairy cows are examined and compared with experimental studies. The simulations describe realistically the effects of nutritional glucose supply on the ovulatory cycle of dairy cattle.

CONCLUSIONS

The mathematical model enables the user to explore the relationship between nutrition and reproduction by running simulations and performing parameter studies. Regarding its applicability, this work is an early attempt towards developing in silico feeding strategies and may eventually help to refine and reduce animal experiments.

REVIEWERS

This article was reviewed by John McNamara and Tin Pang (nominated by Martin Lercher).

Mathematical modeling of the female reproductive system: from oocyte to delivery

From ovulation to delivery, and through the menstrual cycle, the female reproductive system undergoes many dynamic changes to provide an optimal environment for the embryo to implant, and to develop successfully. It is difficult ethically and practically to observe the system over the timescales involved in growth and development (often hours to days). Even in carefully monitored conditions clinicians and biologists can only see snapshots of the development process. Mathematical models are emerging as a key means to supplement our knowledge of the reproductive process, and to tease apart complexity in the reproductive system. These models have been used successfully to test existing hypotheses regarding the mechanisms of female infertility and pathological fetal development, and also to provide new experimentally testable hypotheses regarding the process of development. This new knowledge has allowed for improvements in assisted reproductive technologies and is moving toward translation to clinical practice via multiscale assessments of the dynamics of ovulation, development in pregnancy, and the timing and mechanics of delivery. WIREs Syst Biol Med 2017, 9:e1353. doi: 10.1002/wsbm.1353 For further resources related to this article, please visit the WIREs website.

Modeling the Male Reproductive Endocrine Axis: Potential Role for a Delay Mechanism in the Inhibitory Action of Gonadal Steroids on GnRH Pulse Frequency

We developed a compartmental model so we could test mechanistic concepts in the control of the male reproductive endocrine axis. Using SAAM II computer software and a bank of experimental data from male sheep, we began by modeling GnRH-LH feed-forward and LH-T feedback. A key assumption was that the primary control signal comes from a hypothetical neural network (the PULSAR) that emits a digital (pulsatile) signal of variable frequency that drives GnRH secretion in square wave-like pulses. This model produced endocrine profiles that matched experimental observations for the testis-intact animal and for changes in GnRH pulse frequency after castration and T replacement. In the second stage of the model development, we introduced a delay in the negative feedback caused by the aromatization of T to estradiol at the brain level, a concept supported by empirical observations. The simulations showed how changes in the process of aromatization could affect the response of the pulsatile signal to inhibition by steroid feedback. The sensitivity of the PULSAR to estradiol was a critical factor, but the most striking observation was the effect of time delays. With longer delays, there was a reduction in the rate of aromatization and therefore a decrease in local estradiol concentrations, and the outcome was multiple-pulse events in the secretion of GnRH/LH, reflecting experimental observations. In conclusion, our model successfully emulates the GnRH-LH-T-GnRH loop, accommodates a pivotal role for central aromatization in negative feedback, and suggests that time delays in negative feedback are an important aspect of the control of GnRH pulse frequency.

Milk Production and Fertility in Cattle

Evolutionary biology provides reasons for why the intensive selection for milk production reduces reproductive success rates. There is considerable exploitable genetic variation in reproductive performance in both dairy and beef cattle, and examination of national genetic trends demonstrates that genetic gain for both reproductive performance and milk production is possible in a well-structured breeding program. Reproductive failure is often postulated to be a consequence of the greater negative energy balance associated with the genetic selection for increased milk production. However, experimental results indicate that the majority of the decline in reproductive performance cannot be attributed to early lactation energy balance, per se; reproductive success will, therefore, not be greatly improved by nutritional interventions aimed at reducing the extent of negative energy balance. Modeling can aid in better pinpointing the key physiological components governing reproductive success and, also, the impact of individual improvements on overall fertility, helping to prioritize variables for inclusion in breeding programs.

Modeling endocrine regulation of the menstrual cycle using delay differential equations

This article reviews an effective mathematical procedure for modeling hormonal regulation of the menstrual cycle of adult women. The procedure captures the effects of hormones secreted by several glands over multiple time scales. The specific model described here consists of 13 nonlinear, delay, differential equations with 44 parameters and correctly predicts blood levels of ovarian and pituitary hormones found in the biological literature for normally cycling women. In addition to this normal cycle, the model exhibits another stable cycle which may describe a biologically feasible "abnormal" condition such as polycystic ovarian syndrome. Model simulations illustrate how one cycle can be perturbed to the other cycle. Perturbations due to the exogenous administration of each ovarian hormone are examined. This model may be used to test the effects of hormone therapies on abnormally cycling women as well as the effects of exogenous compounds on normally cycling women. Sensitive parameters are identified and bifurcations in model behavior with respect to parameter changes are discussed. Modeling various aspects of menstrual cycle regulation should be helpful in predicting successful hormone therapies, in studying the phenomenon of cycle synchronization and in understanding many factors affecting the aging of the female reproductive endocrine system.

Computational modelling of bovine ovarian follicle development

Background

The development of ovarian follicles hinges on the timely exposure to the appropriate combination of hormones. Follicle stimulating hormone (FSH) and luteinizing hormone (LH) are both produced in the pituitary gland and are transported via the blood circulation to the thecal layer surrounding the follicle. From there both hormones are transported into the follicle by diffusion. FSH-receptors are expressed mainly in the granulosa while LH-receptors are expressed in a gradient with highest expression in the theca. How this spatial organization is achieved is not known. Equally it is not understood whether LH and FSH trigger distinct signalling programs or whether the distinct spatial localization of their G-protein coupled receptors is sufficient to convey their distinct biological function.

Results

We have developed a data-based computational model of the spatio-temporal signalling processes within the follicle and (i) predict that FSH and LH form a gradient inside the follicle, (ii) show that the spatial distribution of FSH- and LH-receptors can arise from the well known regulatory interactions, and (iii) find that the differential activity of FSH and LH may well result from the distinct spatial localisation of their receptors, even when both receptors respond with the same intracellular signalling cascade to their ligand.

Conclusion

The model integrates the large amount of published data into a consistent framework that can now be used to better understand how observed defects translate into failed follicle maturation.

Evaluation of growth models for follicle development and ovulation in Lusitano mares

Several growth models are commonly used in the biological sciences, to model the follicle growth occurring in the estrous cycle. The aim of this project was to find the model that best fit the follicular size growth data for Lusitano mares. Retrospective data collected from reproduction book records of n=84 mares and n=124 cycles was used to find the series to be fitted to the models. The exponential, Gompertz, logistic, von Bertalanffy, Richards and Weibull models were used, and the most parsimonious and best fit was achieved with the logistic model (r(2)=0.999). The logistic model fits the Lusitano mare's follicle size growth data very well and its parameters were also shown to have a credible biological interpretation.

A mathematical model of the bovine oestrous cycle: simulating outcomes of dietary and pharmacological interventions

A mathematical model was constructed to simulate the bovine oestrous cycle by using nonlinear differential equations to describe the biological mechanisms which regulate the cycle. The model predicts circulating concentrations of gonadotrophin-releasing hormone, follicle-stimulating hormone, luteinizing hormone, oestradiol, inhibin and progesterone. These hormones collectively provide control and feedback mechanisms between the hypothalamus, pituitary gland and ovaries, which regulate ovarian follicular dynamics, corpus luteum function and ovulation. When follicular growth parameters are altered, the model predicts that cows will exhibit either two or three follicular waves per cycle, as seen in practice. Changes in other parameters allow the model to simulate: effects of nutrition on follicle recruitment and size of the ovulatory follicle; effects of negative energy balance on postpartum anoestrus; and effects of pharmacological intervention on hormone profiles and timing of ovulation. It is concluded that this model provides a sound basis for exploring factors that influence the bovine oestrous cycle in order to test hypotheses about nutritional and hormonal influences which, with further validation, should help to design dietary or pharmacological strategies for improving reproductive performance in cattle.

Evaluation of two dairy herd reproductive performance indicators that are adjusted for voluntary waiting period

Background

Overall reproductive performance of dairy herds is monitored by various indicators. Most of them do not consider all eligible animals and do not consider different management strategies at farm level. This problem can be alleviated by measuring the proportion of pregnant cows by specific intervals after their calving date or after a fixed time period, such as the voluntary waiting period. The aim of this study was to evaluate two reproductive performance indicators that consider the voluntary waiting period at the herd. The two indicators were: percentage of pregnant cows in the herd after the voluntary waiting period plus 30 days (PV30) and percentage of inseminated cows in the herd after the voluntary waiting period plus 30 days (IV30). We wanted to assess how PV30 and IV30 perform in a simulation of herds with different reproductive management and physiology and to compare them to indicators of reproductive performance that do not consider the herd voluntary waiting period.

Methods

To evaluate the reproductive indicators we used the SimHerd-program, a stochastic simulation model, and 18 scenarios were simulated. The scenarios were designed by altering the reproductive management efficiency and the status of reproductive physiology of the herd. Logistic regression models, together with receiver operating characteristics (ROC), were used to examine how well the reproductive performance indicators could discriminate between herds of different levels of reproductive management efficiency or reproductive physiology.

Results

The logistic regression models with the ROC analysis showed that IV30 was the indicator that best discriminated between different levels of management efficiency followed by PV30, calving interval, 200-days not-in calf-rate (NotIC200), in calf rate at100-days (IC100) and a fertility index. For reproductive physiology the ROC analysis showed that the fertility index was the indicator that best discriminated between different levels, followed by PV30, NotIC200, IC100 and the calving interval. IV30 could not discriminate between the two levels.

Conclusion

PV30 is the single best performance indicator for estimating the level of both herd management efficiency and reproductive physiology followed by NotIC200 and IC100. This indicates that PV30 could be a potential candidate for inclusion in dairy herd improvement schemes.

A differential equation model to investigate the dynamics of the bovine estrous cycle

To investigate physiological factors affecting fertility of dairy cows, we developed a mechanistic mathematical model of the dynamics of the bovine estrous cycle. The model consists of 12 (delay) differential equations and 54 parameters. It simulates follicle and corpus luteum development and the periodic changes in hormones levels that regulate these processes. The model can be used to determine the level of control exerted by various system components on the functioning of the system. As an example, it was investigated which mechanisms could be candidates for regulation of the number of waves of follicle development per cycle. Important issues in model building and validation of our model were parameter identification, sensitivity analysis, stability, and prediction of model behavior in different scenarios.